First, in some manifolds, \(c\) -concave functions form a convex space, that is convex combination of \(c\) -concave functions is again \(c\) -concave. Examples of such spaces include Euclidean spaces, spheres [1]}, and product of spheres (e.g., tori) [2]}. One possibility to enrich our discrete \(c\) -concave model in such spaces is to convex combine and compose multiple \(c\) -concave potentials which preserves \(c\) -concavity, similar in spirit to ICNN [3]}. In more detail, we define the \(c\) -concave potential of a single block \(\varphi _j\) , \(j\in [T]\) , to be a convex combination and composition of several discrete \(c\) -concave functions. For brevity let \(\varphi =\varphi _j\) , and define \(\varphi =\psi _K\) , where \(\psi _K\)  is defined by:
\(\begin{aligned}\psi _0 &= 0 , \\\psi _{k} &= (1-w_{k-1})\phi _{k-1} + w_{k-1} \sigma ( \psi _{k-1}),\end{aligned}\) 
